The invention is based on a brake system for vehicle combinations such as truck-trailers or tractor-trailers, as defined hereinafter. A brake system is already known (German Offenlegungsschrift 37 03 639) in which the electrical energy is supplied to the brake apparatus located in the trailer by the tractor. Because of the great length of the vehicle combination, the supply lines are quite long. When the brake apparatus comes into operation, relatively high currents flow in the lines between the tractor and the trailer. The line resistance causes a drop in voltage, which may impair safe operation of the brake apparatus, especially in the case of an anti-skid (ABS) and/or traction control system.